Valence quark contribution for theγN→Δquadrupole transition extracted from lattice QCD

Starting with a covariant spectator quark model developed for the nucleon $N$ and the $\Delta$ in the physical pion mass region, we extend the predictions of the reaction $\gamma N\to \Delta$ to the lattice QCD regime. The quark model includes $S$ and $D$ waves in the quark-diquark wave functions. Within this framework, it is the $D$-wave part in the $\Delta$ wave function that generates nonzero valence contributions for the quadrupole form factors of the transition. Those contributions are however insufficient to explain the physical data, since the pion cloud contributions dominate. To separate the two effects, we apply the model to the lattice regime in a region where the pion cloud effects are negligible and adjust the $D$-state parameters directly to the lattice data. This process allows us to obtain a better determination of the $D$-state contributions. Finally, by adding a simple parametrization of the pion cloud, we establish the connection between the experimental data and the lattice data.